{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "identity = lambda i: i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def heapify(heap, key=identity):\n",
    "    n = len(heap)\n",
    "    for i in reversed(range(n // 2)):\n",
    "        sift_down(heap, i, n, key=key)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def heap_push(heap, value, key=identity):\n",
    "    i = len(heap)\n",
    "    heap.append(value)\n",
    "    sift_up(heap, i, key=key)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def heap_pop(heap, key=identity):\n",
    "    item, heap[0] = heap[0], heap[-1]\n",
    "    del heap[-1]\n",
    "    heap and sift_down(heap, 0, len(heap), key=key)\n",
    "    return item"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sift_down(heap, i, n, key=identity):\n",
    "    # item to be sifted\n",
    "    item = heap[i]\n",
    "    item_key = key(item)\n",
    "\n",
    "    while True:\n",
    "        smallest, k = item_key, i\n",
    "        j = 2 * i + 1\n",
    "\n",
    "        # left child\n",
    "        if j < n:\n",
    "            left_key = key(heap[j])\n",
    "            if left_key < smallest:\n",
    "                smallest, k = left_key, j\n",
    "\n",
    "        # right child\n",
    "        if j + 1 < n and key(heap[j + 1]) < smallest:\n",
    "            k = j + 1\n",
    "\n",
    "        # swap or finish\n",
    "        if k != i:\n",
    "            heap[i] = heap[k]\n",
    "            i = k\n",
    "        else:\n",
    "            break\n",
    "\n",
    "    heap[i] = item"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sift_up(heap, i, key=identity):\n",
    "    # item to be sifted\n",
    "    item = heap[i]\n",
    "    item_key = key(item)\n",
    "\n",
    "    while i:\n",
    "        j = i // 2\n",
    "\n",
    "        if item_key < key(heap[j]):\n",
    "            heap[i] = heap[j]\n",
    "            i = j\n",
    "        else:\n",
    "            break\n",
    "\n",
    "    heap[i] = item"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def heap_sort(data, key=identity):\n",
    "    heapify(data, key=key)\n",
    "    \n",
    "    for i in reversed(range(len(data))):\n",
    "        data[0], data[i] = data[i], data[0]\n",
    "        sift_down(data, 0, i, key=key)\n",
    "    \n",
    "    data.reverse()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## run"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### priority queues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data1, data2 = [9, 7, 5, 3, 1], [8, 6, 4, 2, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0, 1, 2, 3, 4, 5, 6, 7, 8, 9, "
     ]
    }
   ],
   "source": [
    "heapify(data1)\n",
    "heapify(data2)\n",
    "\n",
    "while data1 or data2:\n",
    "    data2 and heap_push(data1, heap_pop(data2))\n",
    "    print(heap_pop(data1), end=', ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### string array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = ['hello', 'bye', 'good-bye', 'hi', 'hey!', 'good night']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['bye', 'good night', 'good-bye', 'hello', 'hey!', 'hi']"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "heap_sort(data)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['hi', 'bye', 'hey!', 'hello', 'good-bye', 'good night']"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "heap_sort(data, key=len)\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### string array treated as hexadecimal values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = ['ff', '100', 'ac', '5', '99cc', '393', '000152']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['000152', '100', '393', '5', '99cc', 'ac', 'ff']"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "heap_sort(data)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['5', 'ac', 'ff', '100', '000152', '393', '99cc']"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "heap_sort(data, key=lambda i: int(i, 16))\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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